How to simulate adhesion of water?

Hi, I'm trying to simulate precipitation falls on a tree and forms a stream of water flow down along the branch and stem, I tried to use a particle system and it seems particles would either bumped away or stick to the tree, although these two can be useful to simulate throughfall and interception, but mainly I want to simulate the stemflow, where water flows down to the water. To simplify the scene, imagine you pour water slowly onto a tilted stick, water would flow along with the stick for a while then drop to the ground, this is the kind of scene I want to simulate, but after trying different way I still have no success, could anyone help me with this? Much thanks.